Experimental study of gasoline-air mixture explosion in imitated vertical dome oil tank
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摘要: 为探究立式拱顶油罐内油气体积分数、点火位置和液位对爆炸超压特性参数与火焰发展的影响规律，开展了一系列的实验研究，得到以下结果：（1）1.7%是任一工况下的最危险油气体积分数，内场超压发展都可以分为超压上升、超压泄放和振荡衰减3个阶段。爆炸过程中CH、C2、OH等自由基的生成和空间分布，使得不同初始油气体积分数下或不同爆炸阶段的火焰呈现不同的颜色变化。（2）点火位置对油气爆炸超压特性参数的影响较大，位置越靠下，爆炸威力越大。罐底中心点火时，内外场平均升压速率取得最大值，分别为0.46和0.05 MPa/s。（3）液位变化对油气爆炸内外场超压的影响较大，油罐侧壁上部位置点火时，50%液位是最危险的液位。任意液位下外场超压随比例距离的增大都呈现幂指数衰减规律，不同液位下油气爆炸外场冲击波超压峰值与距离和油气混合物体积的关系可以用一个公式统一表示。相比于气相空间，液相空间的超压变化具有延后性、负压增强和振荡衰减更快的特点。Abstract: To investigate the influence of gasoline-air mixture volume fraction, ignition position and liquid level on explosion overpressure parameters and flame development in vertical dome oil tank, a series of experiments with nine initial hydrocarbon volume fractions, four ignition positions and five liquid levels were carried out in a transparent imitated oil tank. Dynamic data acquisition system and high-speed camera were employed to detect the changes of internal and external field pressure, and to record the transformation of flame shape. The following results were found. (1) 1.7% is the most dangerous gasoline-air mixture volume fraction under any working condition. The development of overpressure in the inner field can be divided into three stages: overpressure rise, overpressure release and oscillation attenuation. The formation and spatial distribution of free radicals such as CH, C2 and OH during the explosion process make the flame show different color changes under different initial volume fractions or at different explosion stages. (2) Ignition position has a great influence on explosion overpressure parameters. The lower the ignition position is, the greater the explosion power is. When the ignition position is in the center of the bottom of the tank, the average pressure boost rate of the internal and external fields reaches the maximum value, being 0.464 MPa/s and 0.053 MPa/s, respectively. (3) The change of liquid level has a great influence on the overpressure of the internal and external field of oil and gas explosion. When the position ignition is located at the top of the side wall of the oil tank, the 50% liquid level is the most dangerous level. At any liquid level, the outfield overpressure decreases exponentially with the increase of scaled distance. The relationship among the maximum overpressure peak of the outfield shock wave of gasoline-air mixture explosion at different liquid levels, the distance and the volume of gasoline-air mixture can be expressed by a unified expression. Compared with gas space, the overpressure in liquid space has the characteristics of delay, enhancement of negative overpressure and faster oscillation attenuation frequency.
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Key words:
- vertical dome oil tank /
- gasoline-air mixture explosion /
- chemical reaction /
- overpressure /
- flame
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PBX炸药是战斗部杀伤、破坏和动力能源的关键材料，随着现代高性能武器的飞速发展，对提高PBX炸药在各种条件下安全性的要求日益迫切。武器战斗部装药在勤务过程以及终点弹道阶段，可能经受长脉冲、多次高过载作用、压缩、拉伸、往复压-拉、与壳体壁面的摩擦等复杂过程，PBX炸药力学性能与损伤机理的差异往往导致炸药后续的反应特性与起爆机制的差异，继而对炸药安全性评估产生影响。当前高速侵彻武器装药的安全性评估，除了开展模拟环境条件及综合考核实验，还通过一些基础分解实验获得机理认识和参数参量数据，对影响安全性问题的主控因素进行分析。开展PBX炸药的力学性能与损伤机理研究，可为武器装药的安全性分析提供机理认识与基础数据，是开展炸药安全性研究的重要内容。
近年来，开展了炸药在不同条件下的力学性能与损伤机理研究，主要关注炸药的应力、应变本构关系，考虑应变率和温度的影响，重点关注炸药的动态(中高应变率)力学性能[1-8]，以及力学作用下的损伤模式、损伤与反应特性之间的关系[9-12]等。其中，炸药损伤破坏对其力学性能的影响，特别是PBX炸药在动态压缩过程中表现出的力学性能，与炸药内部损伤演化-破坏变形之间的关联关系，一直是关注的重点。典型PBX炸药是炸药晶体颗粒、黏结剂/钝化剂的混合，炸药表现出的力学性能不仅与内部细观结构密切相关，而且还与炸药多种损伤形式相关。由于力学性能与损伤破坏相互关联的机理相当复杂，难以通过实验直接获得不同载荷阶段对应的损伤破坏状态，目前通常采用数值模拟手段开展相关研究工作。
本文中，采用离散元方法，考虑PBX炸药晶体与黏结剂非均质结构，开展PBX炸药动态压缩过程的数值模拟，获得加-卸载路径下试样应力应变曲线以及相应的损伤破坏图像。
1. 数值模拟方法
PBX炸药的Hopkinson压杆实验是常见的动态压缩实验，典型的应力应变曲线如图 1所示。曲线一般包含弹性、强化、软化阶段，通过高速摄影可以获得炸药在不同曲线阶段发生的宏观破坏图像，但炸药内部细观响应过程无法获取。采用离散元方法，可模拟应力应变曲线的典型阶段，再现炸药的SHPB动态压缩过程。离散元法(discrete element method, DEM)的基本思想是，把不连续体或连续体离散为具有一定物理意义的独立“微元”或“粒子”，相邻的单元之间存在一种或几种作用力，单元的运动受牛顿第二运动定律支配。它适合于界面弱连接的非连续介质问题或连续体到非连续体转化的断裂、破碎等问题，在开展多组份炸药材料损伤机理模拟研究方面具有算法优势。
计算模型如图 2所示，不规则形状代表HMX晶体，其间的填充物为黏结剂，HMX与黏结剂的质量比约为92:8。HMX平均直径150 μm，离散元单元半径5 μm，黏结剂离散元半径为2 μm，模型总尺寸为1.35 mm×0.67 mm。
采用应力边界需考虑试样两端的入、透射杆长度，这将极大增加计算量。本文中采用飞片在试样两端相向加载的方法，将原SHPB实验的应力边界替代为速度边界，速度分别为v1和v2，为了满足试样的平衡条件，飞片速度满足以下关系式：
vi={tv0t0t≤t0v0t>t0i=1,2 式中：t0=2nL/c，L为试样厚度，c为试样的纵波声速，n为声波往返试样内的传播次数，取n=4。
应变率取决于试样两端飞片的速度与试样厚度，˙ε=(v1+v2)/L；试样应力取整个模型单元x方向应力的平均值，应变为厚度方向的变形量与原厚度之比；定义失效单元与总单元数之比为损伤量，即D=m′/m，其中m为计算模型总的离散单元数，m′为失效单元的数，失效单元为所受应变超过最大拉应变的离散单元。
单元间的作用力形式见文献[13]，HMX晶体采用弹脆性模型，黏结剂采用离散元本构方程、朱-王-唐非线性黏弹性模型，其离散元参数见表 1。其中，ρ为密度，c0、λ为冲击绝热参数，αij、m、n为中心势作用力参数，μij为摩擦系数，G为剪切模量，Cn为法向黏性系数，εy为屈服应变，εb为法向断裂应变。
表 1 材料参数Table 1. Material parameters材料 ρ/
(g·cm-3)c0/
(km·s-1)λ aij/GPa m n μij G/
GPaCn/
(Pa·s)εy εb HMX 1.9 2.9 2.06 1.85 1.0 3.0 0.1 10.74 11 0.02 0.005 黏结剂 1.1 2.3 1.70 7.80 1.0 2.0 0.1 6.80 11 0.10 0.020 2. 模拟结果
2.1 弹性阶段
通过人为改变加载脉宽，使试样处于加载-卸载状态，计算可获得应力应变曲线以及对应试样损伤破坏图像。弹性段加-卸载的应力应变曲线以及应力时间曲线如图 3所示，试样内部的应力分布与细观结构演化如图 4所示。即使试样整体处于应力平衡状态，由于PBX炸药为非均质复合材料，炸药细观结构的应力状态呈现非均匀分布，局部应力有高有低，计算获得试样平均应力峰值约18 MPa(见图 4(a))，但炸药局部区域的真实峰值应力却达50 MPa(见图 4(b))。
图 4 弹性阶段初期的应力分布与细观结构Figure 4. Stress distribution and meso-structure at early elastic stage炸药晶体所受应力多大于黏结剂，晶体间的应力以应力桥形式传递，应力局域化现象显著，峰值应力多出现在炸药晶体间的接触处。加载过程，整个试样发生弹性变形阶段，卸载后，试样基本恢复初始状态(见图 4(c))。
继续加-卸载，应力曲线如图 5所示，不同时刻内部应力分布与细观结构如图 6所示。试样应力的非均匀分布明显增强，试样内部以应力桥形式传递应力持续增强，局域化现象更显著，侧壁出现局部损伤破坏。90 μs后，应力沿应力桥路径卸载，幅值逐步降低，侧壁的局部损伤破坏加剧，局部颗粒出现分离现象，其余部分承力并发生卸载回滞。
图 6 弹性阶段后期的应力分布与细观结构Figure 6. Stress distribution and meso-structure at later elastic stage2.2 强化阶段
强化阶段加-卸载的应力曲线如图 7所示，不同时刻内部应力分布与细观结构如图 8所示。试样局部损伤破坏增加，侧壁分离现象加剧；黏结剂所受应力增加，不再承力的损伤破坏区域与继续承力区域边界逐渐明显。在140μs时刻卸载后，应力仍沿应力桥路径卸载，侧壁的分离现象加剧，承力区域呈现出两端大中部小的哑铃状。
图 8 强化阶段的应力分布与细观结构Figure 8. Stress distribution and meso-structure at hardening stage2.3 软化阶段
应变软化初期阶段加-卸载的应力曲线、不同时刻内部应力分布与细观结构，如图 9~10所示。在140 μs时刻达到曲线应力峰值(56 MPa)后，出现大面积的失稳破坏，未破坏的承力区域逐渐小于损伤破坏区域，未破坏区域的真实应力仍大于峰值应力。在190 μs时刻发生卸载后，损伤破坏现象仍持续加剧，卸载回滞主要由未破坏的承力部分引起。
图 10 应变软化阶段初期的应力分布与细观结构Figure 10. Stress distribution and meso-structure at early strain softening stage应变软化后期加载的应力曲线、不同时刻内部应力分布与细观结构，如图 11~12所示。伴随着损伤破坏区域的增加，未破坏的真实承力区域越来越少，而计算应力采用面积仍沿用初始面积，导致平均化后试样的应力减小，应变继续增加，形成应变软化阶段。图 11中，红色曲线为光滑处理过的应力曲线，蓝色曲线为损伤变量曲线。从图中可知，弹性阶段损伤较小，强化阶段逐渐增大，应力曲线软化阶段达到最大值。
图 12 应变软化阶段后期的应力分布与细观结构Figure 12. Stress distribution and meso-structure at later strain softening stage3. 小结
采用离散元方法，考虑了PBX炸药多组份结构，对炸药应力应变曲线不同阶段进行了细观数值模拟研究，获得了加-卸载路径下试样应力应变曲线以及相应的损伤破坏图像。模拟结果表明：在动态压缩过程中，虽然PBX炸药处于整体应力平衡，由于PBX高度非均质性，内部应力并不均匀，晶体高于黏结剂，应力集中区域出现在晶体接触间，以应力桥形式传递；应力曲线为试样整体平均，即使达到曲线峰值应力后，试样内局部所受真实应力仍可能高于峰值应力；出现卸载回滞曲线的试样发生局部损伤破坏，而完全软化曲线的试样发生整体失稳破坏。
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图 3 模拟油罐油气爆炸内场测点超压时序曲线
Figure 3. The time history of overpressure measurement points in the field of gasoline-air mixture explosion in simulated tank
图 4 内外场平均升压速率与初始油气体积分数的关系
Figure 4. Average overpressure rise rate in the internal and external fields at different initial volume fractions
图 5 不同初始体积分数的油气爆炸火焰传播图像
Figure 5. Images of flame propagation of gasoline-air mixture explosion at different initial volume fractions
图 6 不同点火位置油气爆炸罐内火焰传播图像
Figure 6. Images of flame propagation of gasoline-air mixture explosion inside the tank at different ignition locations
图 7 75%液位油气爆炸内外场最大超压峰值与初始油气体积分数的关系
Figure 7. The maximum overpressure peak in the internal and external field of gasoline-air mixture explosion with different initial volume fraction at 75% liquid level
图 8 100%液位油气爆炸内外场最大超压峰值与初始油气体积分数的关系
Figure 8. The maximum overpressure peak in the internal and external field of gasoline-air mixture explosion with different initial volume fraction at 100% liquid level
图 9 油气爆炸内外场最大超压峰值与油气混合物体积的关系
Figure 9. Relationship between the maximum overpressure peak in the internal and external field of gasoline-air mixture explosion and the volume of gasoline-air mixture
图 10 油罐外场最大超压峰值分布
Figure 10. Distribution of the maximum overpressure peak in the external field of the tank
图 11 不同液位外场最大超压峰值与比例距离的关系
Figure 11. Relationship between the maximum overpressure inside the tank and the scaled distance at different liquid levels
图 12 50%液位油罐油气爆炸内场测点超压时序曲线
Figure 12. Time series curve of overpressure inside tank of gasoline-air mixture explosion at 50% liquid level
图 13 油气爆炸油罐内场压力传播图
Figure 13. Pressure propagation diagram of gasoline-air mixture explosion inside tank
图 14 不同液位油气爆炸火焰传播图像
Figure 14. Images of flame propagation of gasoline-air mixture explosion at different liquid levels
表 1 不同初始体积分数下的油气爆炸内场超压参数
Table 1. Internal field overpressure parameters of gasoline-air mixture explosion at different initial volume fractions
φCH/% pin,max/kPa tin,max/ms (dp/dt)in,ave/(MPa·s−1) 0.9 20.37 212 0.10 1.1 26.71 103 0.26 1.4 27.02 70 0.39 1.6 27.86 69 0.40 1.7 31.59 68 0.46 1.8 27.44 90 0.31 2.0 24.67 115 0.22 2.3 22.98 194 0.12 2.6 20.26 462 0.04 
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表 2 不同初始体积分数下油气爆炸罐内火焰强度最大峰值和形成时间
Table 2. Maximum peak flame intensity and time of formation in the tank at different initial volume fractions
φCH/% Imax/mV tmax/ms 0.9 14 483 1.1 69 238 1.4 190 175 1.6 137 184 1.7 107 188 1.8 70 238 2.0 97 313 2.3 162 485 2.6 161 798
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表 3 不同点火位置的油气爆炸超压参数
Table 3. Overpressure parameters of gasoline-air mixture explosion at different ignition locations
点火位置 pin,max/kPa tin,max/ms (dp/dt)in,ave/(MPa·s−1) pext,max /kPa text,max/ms (dp/dt)ext,ave/(MPa·s−1) 上部点火 21.91 64 0.34 0.18 5 0.04 中部点火 22.60 64 0.35 0.27 9 0.03 下部点火 26.22 65 0.40 0.37 12 0.03 底部点火 31.59 68 0.47 0.53 10 0.05
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表 4 不同液位下不同初始体积分数油气爆炸内外场最大超压峰值
Table 4. The maximum overpressure peak in the internal and external field of gasoline-air mixture explosion with different initial volume fraction at different liquid levels
φCH/% 75%液位 100%液位 pin, max/kPa pext, max /kPa pin, max/kPa pext, max /kPa 0.9 19.70 0.11 19.88 0.05 1.1 20.95 0.12 20.76 0.09 1.4 22.94 0.17 20.91 0.09 1.6 23.29 0.18 21.41 0.16 1.7 24.02 0.22 22.47 0.18 1.8 23.89 0.20 21.08 0.15 2.0 22.39 0.19 20.63 0.09 2.3 22.55 0.15 20.15 0.07 2.6 19.95 0.13 20.16 0.03
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表 5 不同液位油气爆炸内场超压参数
Table 5. Overpressure parameters inside tank of gasoline-air mixture explosion at different liquid levels
液位/% pin,max/kPa tin,max/ms (dp/dt)in,ave/(MPa·s−1) 0 21.91 64 0.34 25 23.30 63 0.37 50 25.40 59 0.43 75 24.02 56 0.43 100 22.47 53 0.42
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